In this paper, we consider a regularized variational inequality for set-valued maps which is defined by means of a Bregman function and prove the existence of its solution by using the equilibrium problem technique. We use regularization technique to prove the existence of solutions of variational inequalities for set-valued maps under premonotonicity assumption which is weaker than the monotonicity of the set-valued map involved in the formulation of the problem. We establish sufficient conditions which guarantee that the sequence of strong solutions of regularized problem admits weak cluster points, and each weak cluster point of this sequence is a strong solution of the variational inequality.
|State||Published - Feb 2022|
Bibliographical noteFunding Information:
Authors would like to express their gratitude to the anonymous referee and the handling editor for their careful reading and comments led to improve the quality of the paper. This research was done during the visit of the second and the third author at King Fahd University of Petrol and Minerals (KFUPM), Dhahran, Saudi Arabia, and was supported by the KFUPM Funded Research Project # IN 161042. Authors are grateful to KFUPM, Dhahran, Saudi Arabia for providing excellent research facilities to carry out this research work. The research of the third author was also supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project Number PN-III-P4-ID-PCE-2016-0190.
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
- Bregman function
- Premonotone mappings
- Variational inequalities
- Weak approximation
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (all)